Picosecond Time-Resolved Optical Studies of Plasma Formation and Lattice Heating in Silicon
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PICOSECOND TIME-RESOLVED OPTICAL STUDIES OF PLASMA FORMATION AND LATTICE HEATING IN SILICON
L. A. LOMPRE,* J. M. LIU,** H. KURZ AND N. BLOEMBERGEN Division of Applied sciences, Harvard University, Cambridge, MA 02138; *C.E.N. Saclay, DPh.G./S.P.A.S., 91191 Gif-surYvette, France; **Department of Electrical and Computer Engineering, Bell Hall, SUNY at Buffalo, Amherst, NY 14260
ABSTRACT Time-resolved studies of reflectivity and transmission at 0.532 vim,1.064 vm and 2.8 vimof thin silicon films following irradiation with ps pulses at 0.532 vm have been performed. The formation of the electron-hole plasma and the evolution of lattice temperature is investigated as a function of pump fluence and time delay. Quantitative determination of the plasma densities and lattice temperature up to the melting temperature shows that the maximum plasma density is 3 limited to - 1 x 1021 cmby Auger recombination even on a time scale of picoseconds at fluences sufficient to cause the phase transition. The thermal nature of the phase transition is confirmed.
Numerous investigations of the change in optical properties of silicon have been carried out as a function of picosecond irradiation fluence (1-4]. These data indicate melting of the surface when the pulse fluence exceeds a critical threshold value. This paper shows that more quantitative information about the lattice temperature and the electron-hole plasma kinetics can be obtained by varying the wavelength of the probing beam and its time delay with respect to the heating pulse. The real part of the dielectric function at a probing frequency w below the direct bandgap, 61 = n
2
L
(T,N)fl - k (T,N)]
-
AN
(1)
where 2
4r~e
/1 l1
increases with the lattice temperature T due to indirect interband transitions and decreases with the number of electron-hole pairs N. The optical mass, m* = (me + mh )-1 may depend on the structure in the vicinity d of the conduction band minimum and valence band maximum covered by the energetic distribution of the carriers during the time of observation. The imaginary part of the dielectric function 2n2(T,N)kL(T,N) L L
+ BN
(2)
where
B
--47re2 ( ;me
+
•h> )
increases with the temperature T and plasma density N. As a third unknown parameter, the scattering times of the carriers (Te and Th) averaged over their energy distribution come into play. At a wavelength of 532 nm the real part C' reveals the opposing effects Mat. Res. Soc.Symp. Proc. Vol. 23 (1984) @Elsevier Science Publishing Co., Inc.
S
58
of increasing lattice temperature and increasing plasma density. The imaginary part depends mainly on the lattice temperature, while plasma absorption is negligible at 532 nm (5,6]. By contrast, at 2.8 vm and 1.9 vm both 6' and E" are dominated by plasma effects [7]. Careful comparison between the time-resolved spectra of the reflectivity and transmission at these wavelengths permits the quantitative determination of the lattice temperature and plasma density during and after ps excitations by photons whose energies are about twice as l
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